Space/Time Hacks

• Code Efficiency and Runtime
  • Algorithm Complexity:
  • O(n)
  • O(n^4)
  • Input Data Size:

Over the course of my analysis on the Space Time Lecture I have learned many things, In these hacks I will cover; __.

Code Efficiency and Runtime

While studying Code efficiency and runtime I have discovered 4 things that affect the runtime of a code cell

Algorithm Complexity:

Algorithms that have a higher time complexity, such as those with nested loops or recursion, tend to take longer to execute compared to simpler algorithms. For example, an algorithm that has a time complexity of O(n^4) will take much longer to execute than an algorithm with a time complexity of O(n).

O(n)

import time

def linear_search(arr, target):
    start = time.time()
    n = len(arr)
    for i in range(n):
        if arr[i] == target:
            end = time.time()
            print(f"Time taken: {end - start}")
            return i
    end = time.time()
    print(f"Time taken: {end - start}")
    return -1

arr = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
target = 7
index = linear_search(arr, target)
print(f"Target {target} found at index {index}")

Time taken: 1.6689300537109375e-06
Target 7 found at index 6

O(n^4)

import time

def slow_algorithm(n):
    start = time.time()
    result = 0
    for i in range(n):
        for j in range(n):
            for k in range(n):
                for l in range(n):
                    result += i + j * k - l
    end = time.time()
    print(f"Time taken: {end - start}")
    return result

slow_algorithm(100)

Time taken: 17.22603988647461

245025000000

Input Data Size:

The time taken by an algorithm can also depend on the size of the input data. Algorithms that process larger amounts of data tend to take longer to execute than those that process smaller amounts of data. For example, a sorting algorithm that sorts a list of 10,000 items will take longer to execute than one that sorts a list of 10 items.

import random
import time

def sort_list(list_size):
    # Generate a list of random integers with the specified size
    my_list = [random.randint(1, 100) for _ in range(list_size)]

    # Time how long it takes to sort the list
    start_time = time.time()
    sorted_list = sorted(my_list)
    end_time = time.time()

    # Print the sorted list and the time taken to sort it
    print(f"Sorted list of size {list_size}: {sorted_list}")
    print(f"Time taken to sort: {end_time - start_time} seconds")

sort_list(10)       # Should be pretty fast

Sorted list of size 10: [2, 6, 17, 34, 60, 63, 74, 80, 88, 93]
Time taken to sort: 3.0994415283203125e-06 seconds

sort_list(1000000)     # Should take a bit longer

Sorted list of size 1000000: [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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Time taken to sort: 0.16831612586975098 seconds

sort_list(5000000)    # Should take even longer

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